OpenAI has hardly borrowed anything. They have a $4B revolving credit line but have hardly touched it. They haven't issued any bonds.
Investment isn't debt.
The rates environment directly dictates what capital is available to OpenAI and at what terms. When potential investors can get x% virtually guaranteed, then they are less willing to give cash for equity to OpenAI.
They owe people hundreds of billions, possibly even over a trillion. They've just been very clever in how they've structured it, so on paper they have low debt.